Attractive and repulsive forces between atoms

My understanding is that, as two hydrogen atoms approach, attraction is stronger initially but repulsion is stronger at shorter distances. Taking the simplistic view that protons and electrons are discrete particles, it seems to me that, no matter how closely the atoms approach, there is a always a configuration in which the proton-electron distances can be smaller than the proton-proton and electron-electron distances. Given this, why should repulsion be stronger than attraction at short distances?

Please allow me to name the each particle, as electron1, proton1 and electron2, proton 2.

You wrote that there is a chance that the electron-proton distance can be shorter than the repulsion terms.

But if your word "electron-proton" distance means the initial combination such as electron1-proton1 or electron2-proton2, then these combination only describe the states of the each isolated hydrogen atom.

These cases may not contribute to reinforce the attractive force between the two hydrogen atoms.

We need to investigate how the two electrons will mingle with each other to cause a molecular formation when the two hydrogen atoms approach.

Thanks for your reply. In response to your suggestion that we look at all combinations of particles we might see the following:

4 attracting interactions:

e1-p1

e2-p2

e1-p2

e2-p1

2 repelling interactions

e1-e2

p1-p2

The larger number of attracting interactions simply adds to the difficulty of seeing why the net interaction would be repulsive at short distances.

As for the question of particle distances... Here is an example of why it appears that there are always configurations in which distances between attracting particles are shorter than those between repelling particles:

Place the particles on a circle with an inscribed square such that the protons are at opposite corners of the square and the electrons similarly. Independent of the size of the circle, the attracting pairs are always closer than the repelling pairs. This would appear to apply whether the electrons are visualized as particles or probability distributions ("clouds"). I've tried to attach a rough sketch of this as a pdf or a jpg but despite the size of the files being quite small the system rejects them. I've attached the pdf to a separate email.

Attachments

Thank you very much for performing this analysis. By inspecting the diagram I sent to ou I observed that the distance between attracting particles in this configuration was shorter than this distance between repelling particles. I concluded that there was a net attractive force. This is confirmed by your analysis.

So it appears that, independent of the distance between hydrogen nuclei (individual protons in this case), there is a configuration of protons and electrons for which the net force is attractive. However, it is a fundamental concept that the net force between hydrogen atoms becomes repulsive at short distances. Why, given the possibility of a net attracting configuration of particles as we've demonstrated, does the force become repelling?

Do you think that we might find the answer by considering the following? Our model indicates that the protons and electrons all lie on a circle, at the points where it is intersected by an inscribed square. Perhaps this is inconsistent with actual nuclear-electron and nuclear-nuclear distances.

As the hydrogen nuclei come closer, an increasing portion of the probability distribution of the electrons comes to lie outside the region between the nuclei. As a result, the average distance between electrons and protons becomes greater. This could also be visualized as charge distributions rather than as discrete particles. But either way, since there is greater distance between positive and negative charge, the attractive force becomes weaker. At the same time, since the protons are closer together, the repulsive force becomes greater. Hence the repulsive force predominates over the attractive force and so there is a net repulsion.

Thanks very much for the discussion! By the way, the reason for my interest arises from my work on a modified approach to explaining chemical thermodynamics for students and the general public. Along the way I've discovered an ongoing need to clarify my own understanding. The ultimate aim is to develop a more understandable and interesting thorough explanation of entropy and free energy.

My way of explaining bond formation involves quite a few preliminary steps. I can't reproduce all of the details here but this is a general outline as well as some initial sense of the explanations of entropy and free energy that I am developing:

I don't think a truly understandable explanation of chemical bonding is possible without clearly establishing fundamental physical concepts first. To accomplish this I begin with point masses rather than atoms because even hydrogen atoms are too complex as a starting point.

I begin by using the rebounding of attracting or repelling point masses to explain positive and negative work, kinetic and potential energy, and conservation of energy.

Then, directly building on these explanations, I then explain how total energy determines whether attracting point masses will rebound or orbit.

Then I apply the same approach to hydrogen atoms. I first explain what happens when hydrogen atoms rebound. This involves positive and negative work by both attracting and repelling force and conservation of energy. I then explain how total energy determines whether the atoms will rebound or bond. This parallels my discussion of rebounding vs. orbiting for attracting point masses.

Up to this point I have used isolated pairs of hydrogen atoms at various energy levels. I next focus on groups of hydrogen atoms and explain how, through energy transfer, a pair of atoms that is initially too high in energy to form a bond can give up energy so that a bond can form.

Going forward from this point, I use the principles so far explained to consider a more realistic chemical reaction: The reaction between hydrogen and chlorine molecules. Using the work-energy foundation established for point masses and hydrogen atoms I track the process for a single reaction event.

Then I focus on a collection of many reactants. I consider their energy distribution. I then apply the same basic physical principles used so far to consider the energy processes involved in the reaction. Energy transfer and entropy concepts are developed to explain why the reaction proceeds as it does and how this is dependent on the particular conditions of the reaction.

My aim is to offer a clear explanation of chemical thermodynamic principles (enthapy, entropy, free energy) developed from the basic physical processes of work and energy.

Once this has been done for the hydrogen-chlorine reaction, the same explanations will be applied to other examples with different enthalpy and entropy parameters.

All of this is set in a larger context that is designed to highlight the key importance of thermodynamic concepts.